Emeritus Professor Bill Hogarth

A simple and accurate procedure is given for solving the infiltration equation for nonlinear diffusivity and conductivity. It overcomes some of the numerical difficulties associated with an earlier procedure given by Hogarth et al. (1989), but confirms the accuracy of their results. © 1992 Williams and Wilkins.

The correlation patterns between air temperature and insolation were investigated for four sites ranging from northern to southern Australia and one site in Venezuela. This investigation was considered as a prior important step for the stochastic generation of these climatic variables as input data for crop models. The use of sunshine hours when insolation data were not available to estimate these correlation patterns was investigated. Data from one location, having simultaneously measured records of both solar radiation and sunshine hours, were used in this study. The correlation coefficients between fractional cloudiness estimated from solar radiation or sunshine hours and the maximum temperature on a given day (TX) and between fractional cloudiness and the difference between the maximum temperature on the same day and the minimum temperature on the next day (TD), were calculated for each 14-day period in the year and for each location. Most of these correlation coefficients displayed seasonal variations specific to each location. A methodology is described whereby these correlations can be preserved whilst synthetically generating weather data for input to models of plant growth. It has been suggested that the preservation of these intercorrelations is important for realism in predictions of crop production. © 1990.

The infiltration equation with a time-dependent surface flux is solved numerically for nonlinear conductivities, using first-integral and shooting techniques. The diffusivity and conductivity are both taken as power laws. The relative accuracy of the numerical technique is obtained by comparison with the case of linear conductivity, where an exact analytical solution exists. An approximate analytical result is given and compared with the solution for nonlinear conductivities from the shooting technique. It is found that the approximate analytical result is an excellent approximation to the exact numerical solution. It is also suggested that the solution obtained here can be used to validate the numerical solution of Richard¿s equation for arbitrary soil properties and arbitrary boundary conditions. © 1989 The Williams & Wilkins.

For specific soil properties the fundamental solution of Fujita (1952b) is extended to include the effect of air movement on horizontal absorption. This exact solution is then used to determine the accuracy and range of applicability of two approximations to the sorptivity with air effects previously presented by Parlange et al. (1982) and Sander and Parlange (1984). The optimal sorptivity of Parlange et al. has very good accuracy while the surface water content ¿s is near saturation but decreases in accuracy as ¿s decreases. The approximate sorptivity of Sander and Parlange, however, proves to be extremely accurate for all ¿s with a maximum error of only 0.5%. Sander and Parlange additionally give an approximation to the water profile which is also shown by comparison with the exact solution to have a maximum error of only 0.5%. The aim of this paper is primarily of a theoretical nature in that we use the exact solution to check the accuracy of the approximate solutions as stated above. Alternatively, the solution may be used for checking the accuracy of numerical models. Copyright 1988 by the American Geophysical Union.

A finite-difference scheme with iterative matrix solution is used to analyze the steady infiltration of water from a spherical cavity. Both conductivity and soil-water diffusivity are taken into account and the method is illustrated for Grenoble sand. Convergence to the numerical solution is slow. A comparison is made with previous analytical solutions.

Analytical solutions are usually easy to apply and useful to understand processes. Unfortunately the non-linearity of Richard's equation restricts exact solutions to a few soil-water diffusivities. A general superposition principle is presented here which can be applied for any appropriate soil-water diffusivity. The resulting solutions are, however, approximate and are applicable in general to describe processes lasting a short time only. For this reason the method seems ideally suited to describe the interaction of abrupt fronts with surfaces. Two examples are considered; one involving a plane front, the other a curved front, to illustrate the simplicity and accuracy of the method.